Geodesic
Regularity of solutions to Dirichlet boundary value problem in domains on a manifold
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 44-49 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The regularity of solutions to the Dirchlet boundary value problem is studied for elliptic differential operators of order $2m$ defined on subdomains of a manifold. Relationships between the smoothness of the right hand side, the boundary, and the solutions are obtained. 
@article{VMUMM_2016_5_a7,
     author = {I. V. Tsylin},
     title = {Regularity of solutions to {Dirichlet} boundary value problem in domains on a manifold},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {44--49},
     year = {2016},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/}
}
TY  - JOUR
AU  - I. V. Tsylin
TI  - Regularity of solutions to Dirichlet boundary value problem in domains on a manifold
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 44
EP  - 49
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/
LA  - ru
ID  - VMUMM_2016_5_a7
ER  - 
%0 Journal Article
%A I. V. Tsylin
%T Regularity of solutions to Dirichlet boundary value problem in domains on a manifold
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 44-49
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/
%G ru
%F VMUMM_2016_5_a7
I. V. Tsylin. Regularity of solutions to Dirichlet boundary value problem in domains on a manifold. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2016), pp. 44-49. http://geodesic.mathdoc.fr/item/VMUMM_2016_5_a7/

[1] Savaré G., “Regularity results for elliptic equations in Lipschitz domains”, J. Funct. Anal., 152 (1998), 176–201 | DOI | MR | Zbl

[2] Stepin A.M., Tsylin I.V., “O kraevykh zadachakh dlya ellipticheskikh operatorov v sluchae oblastei na mnogoobraziyakh”, Dokl. RAN, 463:2 (2015), 144–148 | DOI | Zbl

[3] Tsylin I.V., “On the smoothness of solutions to elliptic equations in domains with Holder boundary”, Eurasian Math. J., 6:3 (2015), 76–92 | MR

[4] Muramatu T., “On the dual of Besov spaces”, Publ. Res. Inst. Math. Kyoto Univ., 12:1 (1976), 123–140 | DOI | MR

[5] Bak J.-G., Shkalikov A.A., “Multipliers in dual Sobolev spaces and Schrödinger operators with distribution potentials”, Math. Notes, 71:5 (2002), 587–594 | DOI | DOI | MR | Zbl

[6] Maz'ya V., Shaposhnikova T., Theory of Sobolev multipliers, Springer, Berlin, 2009

[7] Goldman M.L., “Teoremy vlozheniya dlya anizotropnykh prostranstv Nikolskogo–Besova s modulyami nepreryvnosti obschego vida”, Tr. Matem in-ta AN SSSR, 170, 1984, 86–104 | Zbl